What do you like best?
I set MantisBT up and configured it for my team in about an hour and a half. What I like the best is how the program is so straightforward to use, from start to finish. Anyone can jump in, get the information they need, and then get on with their day. There's no slick UI to deal with, it's all simple text.
What do you dislike?
The only thing I'm really not a fan of is how attachments are treated in the tickets. In some other bug trackers I've used, it's possible to slot images in-line with text information. With MantisBT, you have to attach images and there's no way to reference them except for their file name. We type a lot of "see Figure 001" in our tickets, and that seems a little silly.
Recommendations to others considering the product
MantisBT is a cheap, no-frills platform, but it certainly delivers more than it asks of you. If you aren't hung up about fancy UI, and need something right away, this is definitely a program you should look into. I implemented it as a temporary workaround to a problem while researching a "real" solution and discovered this was plenty "real" enough.
What business problems are you solving with the product? What benefits have you realized?
MantisBT has solved a serious communication problem we were having between our Support and Development departments. Support is now able to review existing bugs and log new ones on their own without trying to keep track of everything via email. Development is able to prioritize bugs as they come in, and all interested parties are notified whenever there are updates or resolution has been reached.